This paper describes analytical and simulation models of the population dynamics of transposable elements in randomly mating populations. The models assume a finite number of chromosomal sites that are occupable by members of a given family of elements. Element frequencies can change as a result of replicative transposition, loss of elements from occupied sites, selection on copy number per individual, and genetic drift. It is shown that, in an infinite population, an equilibrium can be set up such that not all sites in all individuals are occupied, allowing variation between individuals in both copy number and identity of occupied sites, as has been observed for several element families in Drosophila melanogaster. Such an equilibrium requires either regulation of transposition rate in response to copy number per genome, a sufficiently strongly downwardly curved dependence of individual fitness on copy number, or both. The probability distributions of element frequencies, generated by the effects of finite population size, are derived on the assumption of independence between different loci, and compared with simulation results. Despite some discrepancies due to violation of the independence assumption, the general pattern seen in the simulations agrees quite well with theory.
Data from Drosophila population studies are compared with the theoretical models, and methods of estimating the relevant parameters are discussed.